Systems and methods for implementing electrically tunable metasurfaces

ABSTRACT

Systems and methods in accordance with embodiments of the invention implement electrically tunable metasurfaces. In one embodiment, an electrically tunable metasurface reflectarray includes: a mirrored surface; a conductive layer; a dielectric layer; where the conductive layer and the dielectric layer are in direct contact, and thereby define a conductor-dielectric interface; a plurality of subwavelength antenna elements; and an electrical power source configured to establish a potential difference between at least one subwavelength antenna element and the mirrored surface; where a potential difference between a subwavelength antenna element and the mirrored surface applies an electric field to a corresponding region of the electrically tunable metasurface reflectarray; where any applied electric fields in conjunction with the geometry and the material composition of each of the subwavelength antenna elements, the conductive layer, and the dielectric layer, enable the electrically tunable metasurface reflectarray to measurably augment the propagation characteristics of incident electromagnetic waves.

CROSS-REFERENCE TO RELATED APPLICATIONS

The current application claims priority to U.S. Provisional ApplicationNo. 61/948,810, filed Mar. 6, 2014, the disclosure of which isincorporated herein by reference.

STATEMENT OF FEDERAL FUNDING

This invention was made with government support under FA9550-12-1-0488 &FA9550-12-1-0024 awarded by the Air Force. The government has certainrights in the invention.

FIELD OF THE INVENTION

The present invention generally relates to the implementation ofelectrically tunable metasurfaces.

BACKGROUND

Metamaterials are generally understood to be artificially synthesizedmaterials that are typically characterized by a repeating pattern ofstructural elements that have characteristic lengths on the order ofless than the wavelength of the waves that they are meant to impact. Forexample, ‘photonic metamaterials’ (also known as ‘opticalmetamaterials’), which are meant to control the propagation of visiblelight, include structural elements that have characteristic lengths onthe order of nanometers—by contrast, the wavelength of visible light ison the order of hundreds of nanometers. Much research has been devotedto developing such materials that have highly counterintuitive, butpractical, optical characteristics—for example, metamaterials havingnegative indices of refraction have been developed and are the subjectof much study.

‘Metasurfaces’ can be thought of as two-dimensional metamaterialsinsofar as they are characterized by a repeating pattern ofsubwavelength structures, and they can offer many of the same advantagesas metamaterials. Indeed, metasurfaces can even be advantageous relativeto metamaterials in many respects. For example, metasurfaces can be madeto more efficiently transmit light as compared to metamaterials.

SUMMARY OF THE INVENTION

Systems and methods in accordance with embodiments of the inventionimplement electrically tunable metasurfaces. In one embodiment, anelectrically tunable metasurface reflectarray includes: a mirroredsurface; a conductive layer; a dielectric layer; where the conductivelayer and the dielectric layer are in direct contact, and thereby definea conductor-dielectric interface; a plurality of subwavelength antennaelements; and an electrical power source configured to establish apotential difference between at least one subwavelength antenna elementand the mirrored surface; where a potential difference between asubwavelength antenna element and the mirrored surface applies anelectric field to a corresponding region of the electrically tunablemetasurface reflectarray; where any applied electric fields inconjunction with the geometry and the material composition of each ofthe subwavelength antenna elements, the conductive layer, and thedielectric layer, enable the electrically tunable metasurfacereflectarray to measurably augment the propagation characteristics ofincident electromagnetic waves.

In another embodiment, an electrically tunable metasurface furtherincludes a second electrical power source configured to establish asecond potential difference between at least one other subwavelengthantenna element and the mirrored surface.

In yet another embodiment, the electrical power source is configured toestablish a plurality of potential differences between a plurality ofsubwavelength antenna elements and the mirrored surface.

In still another embodiment, any applied electric fields in conjunctionwith the geometry and the material composition of each of thesubwavelength antenna elements, the conductive layer, and the dielectriclayer, enable the electrically tunable metasurface reflectarray tomeasurably augment the propagation characteristics of incidentelectromagnetic waves falling within at least some portion of theelectromagnetic spectrum characterized by wavelengths of less than 10μm.

In still yet another embodiment, the at least some portion of theelectromagnetic spectrum is characterized by electromagnetic waveshaving wavelengths less than or equal to wavelengths approximatelycorresponding with those of near infrared electromagnetic waves.

In a further embodiment, when a region of the electrically tunablemetasurface is exposed to an electric field, reflected incidentelectromagnetic waves falling within the at least some portion of theelectromagnetic spectrum exhibit a phase shift based on the magnitude ofthe applied electric field.

In a still further embodiment, the at least some portion of theelectromagnetic spectrum is characterized by electromagnetic waveshaving wavelengths approximately corresponding with those of nearinfrared electromagnetic waves.

In a yet further embodiment, the at least some portion of theelectromagnetic spectrum is characterized by electromagnetic waveshaving wavelengths less than or equal to wavelengths approximatelycorresponding with those of visible light.

In a still yet further embodiment, the at least some portion of theelectromagnetic spectrum is characterized by electromagnetic waveshaving wavelengths approximately corresponding with those of visiblelight.

In another embodiment, the conductive layer includes one of: a nitridebased material; silver; copper; gold; aluminum; an alkali metal; analloy; a transparent conducting alloy; and graphene.

In still another embodiment, the conductive layer comprises indium tinoxide.

In yet another embodiment, the dielectric layer includes a dielectricoxide.

In still yet another embodiment, the dielectric layer comprises aluminumoxide.

In a further embodiment, the mirrored surface includes gold; and atleast one of the plurality of subwavelength antenna elements includesgold.

In a yet further embodiment, when a region of the electrically tunablemetasurface reflectarray is exposed to an electric field, the chargecarrier concentration at the conductor-dielectric interface within thatregion is altered based on the magnitude of the applied electric field,and this alteration causes a phase shift in reflected incidentelectromagnetic waves falling within the at least some portion of theelectromagnetic spectrum.

In a still further embodiment, a variation in charge carrierconcentration from 1×10¹⁹ cm⁻³ to 1×10²¹ cm⁻³ is sufficient to shift thephase of reflected incident electromagnetic waves falling within the atleast some portion of the electromagnetic spectrum by at least 2π.

In a still yet further embodiment, at least one of the plurality ofsubwavelength antenna elements conforms to a rod-shaped geometry.

In another embodiment, at least one of the plurality of subwavelengthantenna elements conforms to a V-shaped geometry.

In still another embodiment, at least one of the plurality ofsubwavelength antenna elements conforms to a split ring geometry.

In yet another embodiment, at least two of the plurality ofsubwavelength antenna elements are connected to the same conductiveelement, which itself is connected to the electrical power source.

In still yet another embodiment, rows of subwavelength antenna elementsare connected to a respective conductive element, which themselves areconnected to the electrical power source.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-1B illustrate a prior art metasurface.

FIGS. 2A-2B illustrate a prior art metasurface reflectarray and itsreflection angles as a function of angles of incidence.

FIGS. 3A-3B illustrate an electrically tunable metasurface reflectarrayincluding rod-shaped subwavelength antenna elements in accordance withcertain embodiments of the invention.

FIG. 4 illustrates prospective materials that can be implemented withina metasurface in accordance with certain embodiments of the invention.

FIGS. 5A-5C illustrate an electrically tunable metasurface that includesan array of gold subwavelength antenna elements, an ITO-Al₂O₃ interface,and a gold mirror, where rows of subwavelength antenna elements are heldat the same electric potential in accordance with certain embodiments ofthe invention.

FIG. 6 illustrates a bottom-gated electrically tunable metasurface inaccordance with an embodiment of the invention.

FIGS. 7A-7C illustrate data demonstrating a resonance split with theapplication of a potential difference, which can be exploited inaccordance with certain embodiments of the invention.

FIGS. 8A-8B illustrate how reflection and phase shift can vary asfunctions of charge carrier concentration and wavelength in accordancewith certain embodiments of the invention.

FIGS. 9A-9B illustrate how reflectance and phase shift can vary as afunction of charge carrier concentration for

DETAILED DESCRIPTION

Turning now to the drawings, systems and methods for implementingelectrically tunable metasurfaces are illustrated. In many embodiments,an electrically tunable metasurface includes an array of subwavelengthantenna elements with complex dielectric functions that areelectro-optically tunable to control the phase and/or amplitude ofreflected and/or transmitted electromagnetic waves including (but notlimited to) electromagnetic waves having wavelengths on the order ofthose of visible light and/or near-infrared (near-IR) light. In numerousembodiments, such metasurfaces are used to implement opticalbeamformers.

Metamaterials and metasurfaces are understood to possess vast potentialfor the robust control of electromagnetic waves. However, much of thedevelopments in this area have been confined to metasurfaces that arelargely fixed in the electromagnetic responses that they generate, andthat are configured to operate over a limited bandwidth. Consequently,there has been much interest in developing ‘tunable’metamaterials/metasurfaces that can have the electromagnetic responsesthat they generate dynamically controlled post-fabrication. Inparticular, there has been significant interest in being able to developtunable metamaterials/metasurfaces that are configured to manipulateelectromagnetic waves that have wavelengths corresponding with nearinfrared waves as well as visible light. In general, it would be usefulto be able control the reflections and refractions emanating fromelectromagnetic waves having wavelengths at or below those of nearinfrared waves. Thus, for instance, “Highly Strained Compliant OpticalMetamaterials with Large Frequency Tunability,” to Pryce et al. (NanoLett. 2010, 10. 4222-4227, DOI:10.1021/nl102684), discloses compliantmetamaterials having a wavelength tunability of approximately 400 nm,greater than the resonant line width at optical frequencies, usinghigh-strain mechanical deformation of an elastomeric substrate tocontrollably modify the distance between the resonant elements. Thedisclosure of “Highly Strained Compliant Optical Metamaterials withLarge Frequency Tunability” is hereby incorporated by reference in itsentirety, especially as it pertains to deforming metamaterials so as totune their electromagnetic response characteristics.

Notwithstanding this demonstration, in many practical applications, itmay not be desirable to have to rely on mechanical deformation in orderto achieve desired electromagnetic response characteristics. Moreover,in many instances it is desirable to exert even more nuanced control ofthe electromagnetic response of a metasurface. For instance, in manyinstances, it may be desirable to be able to locally control theelectromagnetic response characteristics within a metasurface.Additionally, it is worth mentioning that many of the metasurfaces thatare configured to operate on visible light that have been developed sofar are optically inefficient. For example, many existing opticalmetasurfaces have optical efficiencies of less than 10%. As can beappreciated, it can be desirable to implement metasurfaces havingimproved optical efficiencies. While much of the discussion that followsdescribes metamaterials that are used to reflect light to achieveincreased optical efficiencies, it should be appreciated that similartechniques can be utilized to create refractive metasurfaces withdynamically tunable refractive indices.

Accordingly, in many embodiments of the invention, tunable metasurfacesthat are configured to respond to electromagnetic waves havingwavelengths less than 10 μm—e.g. including near infrared and visiblelight—are implemented, where localized electric fields can be used tomanipulate the localized electromagnetic response characteristics of themetasurfaces. Additionally, many embodiments of the invention implementmetasurfaces having improved optical efficiencies. As can beappreciated, such robust metasurfaces can be practically implemented inany of a variety of applications. For example, in many embodiments,optical beamforming metasurfaces are implemented. In a number ofembodiments, the described robust metasurfaces are utilized to realizeholography. In several embodiments, the described robust metasurfacesare utilized to realize animated holography. In number of embodiments,the described robust metasurfaces are used to implement cloakingdevices. Indeed, the described robust metasurfaces can be implemented inany of a variety of applications that can benefit from such robust wavefront shaping ability. Before a detailed description of the structure ofthe metasurfaces is presented, the general understanding of the physicsunderlying metasurfaces phenomena is now presented below.

Generally Understood Metasurface Physics

Before discussing the tunable metasurfaces that are the subject of theinstant application, it is useful to review some of the generallyunderstood physics that govern metasurfaces phenomena. When discussingmetamaterials/metasurfaces phenomena, the generalized version of Snell'slaws are typically used to model the electromagnetic response. Thegeneralized version of Snell's law for refraction can be stated asfollows:

${{n_{t}\sin\;\theta_{t}} - {n_{i}\sin\;\theta_{i}}} = {\left( \frac{\lambda_{0}}{2\;\pi} \right)\frac{d\;\phi}{d\; x}}$where:

-   n_(i) is the index of refraction for a first medium through which    the incident light is transmitted through;-   n_(t) is the index of refraction for a second medium through which    the incident light is transmitted through;-   θ_(i) is the angle of incidence of the incoming light;-   θ_(t) is the angle of refraction of the refracted light as it passes    through the second medium;

$\frac{d\;\phi}{d\; x}$characterizes the change in the phase of the light wave across the planeof incidence; and

-   λ₀ is the wavelength of the incident light.    Similarly, the generalized version of Snell's law for reflection can    be stated as follows:

${{\sin\;\theta_{r}} - {\sin\;\theta_{i}}} = {\left( \frac{\lambda_{0}}{2\;\pi\; n_{i}} \right)\frac{d\;\phi}{d\; x}}$using the same conventions as before, and where θ_(r) is the angle ofreflection of the reflected light. In many circles, the value (dφ/dx) isconsidered to be a wave-vector. Note also that many have characterizedthe generalized versions of Snell's laws as instances of theconservation of momentum.

A discussion of the generalized version of Snell's laws can be found in“Light Propagation with Phase Discontinuities; Generalized Laws ofReflection and Refraction,” to Yu et al. (Science. 2011 Oct. 21; 334(6054): 333-7. doi: 10.1126/science.1210713.). The disclosure of “LightPropagation with Phase Discontinuities; Generalized Laws of Reflectionand Refraction” is hereby incorporated by reference in its entirety,especially as it pertains to the generalized versions of Snell's laws.The refractions and reflections that emanate because of a change inphase across an incident plane can be referred to as ‘anomalousrefractions’ and ‘anomalous reflections’ respectively.

In any case, it is seen from the generalized versions of Snell's lawsthat the angles of refraction and reflection from an incident lightsource are functions of changes in phase across the incident plane.Metasurfaces generally rely on this phenomenon in their operation.Generally, metasurfaces utilize resonators—often in the form ofsubwavelength antenna elements—to cause a change (typically an abruptchange) in the phase of incident light. Such resonators can also be usedto alter the amplitude and polarization of the incident light. Ingeneral, the phase shift (and amplitude and polarization response)caused by a subwavelength antenna element is a function of the geometryof the antenna. Metasurfaces thus far have implemented antenna elementsin a variety of forms including, but not limited to: v-shaped antennaelements, rods, and split ring resonators. As alluded to above, theantenna elements typically have dimensions that are much smaller thanthe wavelengths of the electromagnetic waves that they are meant toimpact.

It should be mentioned that metasurfaces often realize their uniqueproperties because of surface plasmon phenomena. In general, surfaceplasmons, which are charge oscillations of free electrons near a metalsurface, result from the interaction with light and matter, and aretypically generated at a conductor-dielectric interface. Under specificconditions, light couples with the surface plasmons to createself-sustaining, propagating electromagnetic waves, which are known assurface plasmon polaritons. The creation of these surface plasmonpolaritons often relates to the unique optical properties that can beachieved with metasurfaces. Such metasurfaces can be referred to asplasmonic metasurfaces.

FIGS. 1A and 1B illustrate a prior art metasurface including phasedarray antenna elements that demonstrate an ability to shift the phase ofincident infrared electromagnetic waves by any desired extent. Inparticular, FIG. 1A depicts a metasurface 102 including a plurality ofv-shaped phased array antenna elements 104. The highlighted v-shapedantenna elements 106 represent the various antenna elements that areused to demonstrate ‘2π phase coverage.’ In other words, each of thedepicted subwavelength antenna elements basically has the effect ofshifting the phase of the incident infrared electromagnetic wave by acertain amount, with the extent of the shift being based on the geometryof the antenna element. Accordingly, the depicted 8 subwavelengthantenna elements 106 have different geometries, and thereby shift theincoming waves by different amounts. In the illustrated example, thevarying geometries demonstrate an ability to shift the phase of theincident waves by any amount from 0 to 2π, with the shift being based onthe geometry of the antenna element. Note that the antenna elements havelengths of approximately 2 μm—and they are thereby configured to impactinfrared wavelengths (e.g. λ=8 μm). Importantly, as the geometry of theantenna elements is fixed, the respective phase shifts that they causeare also fixed post-fabrication.

FIG. 1B illustrates how incident infrared electromagnetic waves interactwith the antenna array. Note that the propagation direction changes,which is a phenomena not seen in nature.

The above-described physical phenomena underlying metasurface operationcan also be seen in metasurface reflectarrays, where the principleinterest regards reflected light. Typically, such metasurfaces arebounded by a mirror surface, which effectively ‘cancels’ the transmittedlight. Notably, these surfaces can be made to be highly efficient,conserve polarization, and operate at or around optical frequencies.FIGS. 2A-2B illustrate a prior art reflectarray metasurface that isconfigured to impact wavelengths at optical frequencies. In particular,the metasurface 202 includes constituent antenna elements 204 that aresized to cause a particular phase shift. A detailed view of a sub-cell206 is also illustrated, and depicts that the sub-cell includes anantenna element 208 disposed on a dielectric layer 210, which itself isdisposed on a metallic film 212. More specifically, the depicted priorart structure utilizes antenna elements 208 fabricated from gold,dielectric layers 210 fabricated from MgF₂, and a metallic film 212fabricated from gold. The thickness of the gold antenna is approximately30 nm; the thickness of the dielectric layer is approximately 50 nm; andthe thickness of the gold film is approximately 130 nm. The workingwavelength of the depicted structure is approximately 850 nm. Note thatFIG. 2A also illustrates that when the metasurfaces is illuminated withlight having a normal angle of incidence 222, the reflected light224—counterintuitively—reflects at an angle. Such is the effect ofmetasurfaces.

FIG. 2B illustrates a plot of the reflection angle as a function of theangle of incidence. The shaded area 252 indicates the region where theincident light is counterintuitively reflected back towards itself. Notethat the plot indicates that there is a critical angle above which thereis no reflection.

Based upon the above overview of metasurface physics and behavior,opto-electrically tunable metasurfaces that provide dynamic control overthe propagation of electromagnetic waves at wavelengths at or below 10μm including (but not limited to) optical and/or near-IR waves inaccordance with embodiments of the invention are now discussed below.

Electrically Tunable Metasurfaces for Controlling the Propogation ofElectromagnetic Waves having Wavelengths Less than Approximately 10 μm

In many embodiments, electrically tunable metasurfaces for controllingthe propagation of electromagnetic (“EM”) waves having wavelengths lessthan approximately 10 μm—e.g. including near infrared EM waves andvisible EM waves—where electric fields can be locally applied todynamically augment the electromagnetic response characteristics of themetasurface. As can be appreciated from the above discussion, theelectromagnetic response of metasurfaces is strongly correlated with thegeometry of the structure (e.g. the geometry of implemented resonators).As can also be appreciated, the electromagnetic response is also afunction of the constituent materials of the metasurface. In general,the structure and composition of metasurfaces can be tailored toimplement desired electromagnetic response characteristics byselectively implementing particular structures/compositions that cangive rise to the desired electromagnetic response characteristics. Manyembodiments of the instant invention further leverage the newunderstanding that the localized carrier concentration within theconductor of a conductor-dielectric composite within a plasmonicmetasurface can also influence the electromagnetic responsecharacteristics of the metasurface. Thus, in many embodiments of theinvention, a metasurface includes an array of subwavelength antennaelements and a conductor-dielectric interface in an arrangement thatcauses the metasurface to respond to EM waves having wavelengths of lessthan 10 μm, where the application of an electric field augments theelectromagnetic response characteristics of the metasurface. It isbelieved that the applied electric field causes the carrierconcentration at the surface of the conductor-dielectric interface tovary, which in turn modifies the metasurface's electromagnetic responsecharacteristics.

For instance, in many embodiments, electrically tunable metasurfacereflectarrays are implemented. For example, FIGS. 3A-3B illustrate anelectrically tunable metasurface reflectarray that incorporates an arrayof rod-shaped subwavelength antenna elements. In particular, FIG. 3Aillustrates a top-down view of the metasurface 302 that includes anarray of rod-shaped subwavelength antenna elements 304. FIG. 3Billustrates a portion of a cross-sectional view of the metasurface 302that includes a subwavelength antenna element 304. In particular, it isdepicted that the electrically tunable metasurface reflectarray ischaracterized by an underlying mirror, upon which a conductive layer isdisposed, upon which a dielectric layer is disposed. In the illustratedembodiment, the subwavelength antenna element is disposed on thedielectric layer. When an electric field is locally applied to themetasurface, the electromagnetic response characteristics can vary as aconsequence; it is believed that the application of the electric fieldmodifies the charge carrier concentration within the conductive layer atthe conductor-dielectric interface—i.e. within the active conductivelayer region, and that this is what gives rise to the change in theelectromagnetic response of the metasurface. In the illustratedembodiment, it is depicted that a potential difference is directlyapplied between the mirror and the subwavelength antenna element,establishing an electric field. Note that potential differences can beestablished in any of a variety of ways in accordance with embodimentsof the invention. In many embodiments one or more electrical powersources are used to establish potential differences between thesubwavelength antenna elements and the mirrored surface. In manyembodiments an electrical power source can establish a plurality ofpotential differences between a respective plurality of thesubwavelength antenna elements and the mirrored surface. Any of avariety of circuitry can be used to accomplish the application ofpotential difference(s) across the electrically tunable metasurface inaccordance with embodiments of the invention. While the application ofpotential differences has been discussed, it should be clear that anelectric field can be established across electrically tunablemetasurfaces in any of a variety of ways in accordance with manyembodiments of the invention.

Additionally, as can be appreciated, the particular geometry of thesubwavelength antenna elements, and the thickness of the dielectric andconductive layers can be chosen based on the desired electromagneticresponse characteristics. Moreover, the particular materials implementedwithin the layers and subwavelength antenna elements can also impact theelectromagnetic response characteristics of the metasurfacereflectarray. Thus, as can be appreciated, the materials selected forforming the metasurface reflectarray can also be based on the desiredelectromagnetic response. For instance, in some embodiments, theconductive layer includes one of: indium tin oxide, graphene, aconducting nitride, and titanium nitride. “Low-Loss Plasmonicmetamaterials”, by Boltasseva et al. (Science 331, 290 (2011); DOI:10.1126/science. 1198258), discloses considerations in the selection ofmaterials for implementation within metamaterials. “Low-Loss PlasmonicMetamaterials” is hereby incorporated by reference in its entirety,especially as it discloses considerations in the materials selectionprocess in the formation of metamaterials. FIG. 4, extracted from“Low-Loss Plasmonic Metamaterials” illustrates several materials thatcan be utilized in the implementation of metasurface reflectarrays basedon the targeted electromagnetic wavelengths. Similarly, any suitabledielectric layer can be implemented. For example, in many embodiments adielectric oxide is implemented. In several embodiments, Aluminum Oxide(Al₂O₃) is implemented as the dielectric layer. Any suitable materialreferenced in FIG. 4 can be utilized in the implementation ofmetasurface reflectarrays in accordance with embodiments of theinvention. In some embodiments, the implemented materials are those thatare compatible with existing manufacturing infrastructure. For instance,in many embodiments the material of the conductive layer is one that canreadily be incorporated in modern day semiconductor fabrication houses.In general, as can be appreciated, the metasurface depicted in FIGS.3A-3B can be modified in any of a variety of ways based on the desiredelectromagnetic response characteristics and desired operation inaccordance with many embodiments of the invention.

In many embodiments, a plurality of subwavelength antenna elements arein contact with a single conductive element so that they are held at thesame electric potential. In this arrangement, electric fields may beable to be more easily established—e.g. a potential difference can moreeasily be applied between the plurality of subwavelength antennaelements and the mirror. For instance, FIGS. 5A-5C illustrate ametasurface reflectarray that includes rows of subwavelength antennaelements, each connected by a single respective conductive element. Inparticular, FIG. 5A illustrates an isometric view of the electricallytunable metasurface reflectarray. More specifically, FIG. 5A illustratesthe metasurface 502, that includes rod-shaped subwavelength antennaelements 504, which are connected by a conductive element 506, and arethus held at the same electric potential. Thus, FIG. 5A illustrates thata voltage is applied between the underlying mirrored surface and thefirst row of subwavelength antenna elements, and that his voltage can beused to locally modify the electromagnetic response characteristics. Inmany embodiments, different phases can be applied to adjacent rows ofsubwavelength antenna elements to perform optical beamsteering. In otherembodiments, voltages can be applied to modify the phase across thewavefront of reflected light in any manner appropriate to therequirements of a specific application. FIG. 5B illustrates a scanningelectron microscope (SEM) image of the electrically tunable metasurfacereflectarray depicted in FIG. 5A.

FIG. 5C illustrates a portion of the cross-section of the electricallytunable metasurface reflectarray seen in FIGS. 5A-5B. In particular, itis depicted that the metasurface reflectarray is characterized by anunderlying gold mirror, upon which an ITO layer is disposed, upon whichan aluminum oxide—Al₂O₃—dielectric layer is disposed. The goldsubwavelength antenna elements 504 are disposed on top of the Al₂O₃dielectric layer.

The geometry of the illustrated embodiment is characterized as follows:the gold mirror is 130 nm thick; the ITO layer is 16 nm thick; thealuminum oxide layer is 5 nm thick, and the spatial dimensions of thesubwavelength antenna elements are 180 nm×60 nm×50 nm. Accordingly, thedescribed geometry and composition of the structure, establish amagnetic resonance at an electromagnetic wavelength of 1265 nm.

FIG. 5C also depicts that a potential difference is applied between thesubwavelength antenna element and the gold mirror. This allows for theapplication of an electric field across the ITO-Al₂O₃ interface. As willbe elaborated on in greater detail below, it is believed that theelectric field causes a variation in carrier concentration at theITO-Al₂O₃ interface, which in turn can augment the electromagneticresponse characteristics in a desired manner. In other words, it isbelieved that the electric field causes the development of an ‘activeITO’ region having a different charge carrier concentration, which isdepicted in FIG. 5C, that locally augments the electromagnetic responsecharacteristics. However, it should be clear that embodiments of theinvention are not constrained to the actual realization of thisphenomenon. It has been experimentally verified that the electromagneticresponse characteristics of this described metasurface, which isconfigured for near infrared EM waves, can be tuned using an electricfield.

While a specific example of a metasurface reflectarray has beenillustrated in FIGS. 5A-5C and described above, it should be clear thatembodiments of the invention are not constrained to this specificallydescribed structure. As can be appreciated, the structure can bemodified in any of a variety of ways suitable to the desired applicationof the metasurface. For example, while the metasurface reflectarrayincludes rows of subwavelength antenna elements held at the sameelectric potential, in many embodiments, localized electric fields canbe applied to individual subwavelength antenna elements, and thereby beused to more precisely modify the electromagnetic responsecharacteristics of the metasurface. For instance in many embodiments,metasurfaces are implemented such that each of a plurality ofsubwavelength antenna elements is independently addressable using, e.g.control circuitry typically used in a pixelated display. Such aconfiguration can enable extensively robust control over the localizedelectromagnetic response characteristics of a metasurface. In this way,the metasurface can be utilized to perform wavefront shaping in anymanner appropriate to the requirements of specific applicationsincluding (but not limited to) steerable optical beamforming, andholography. Of course, it can be appreciated that electric fields can belocally applied to metasurfaces using any of a variety of techniques inaccordance with embodiments of the invention.

Note that where conventional electrical power sources are used toestablish a potential difference that gives rise to an electric field,power is only significantly consumed when the changing of the electricfield is desired; comparatively little power is used in sustaining theelectric field. Thus, the described electrically tunable metasurfacescan be made to be relatively energy efficient.

Additionally, as can be appreciated, while subwavelength antennaelements having specific dimensions and geometries have been discussedabove, it should be clear that any of a variety of antenna geometriescan be implemented in accordance with embodiments of the invention. Insome embodiments V-shaped antenna elements are implemented. In a numberof embodiments, split ring resonators are implemented. In severalembodiments, rods are implemented as antenna elements. As can beappreciated, the particularly implemented antenna elements can be basedon the desired electromagnetic response characteristics for themetasurface.

Moreover, while a specific layering configuration has been discussed, itshould also be clear that any suitable configuration that allows for theimplementation of a metasurface including a conductor-dielectricinterface that provides a tunable refractive index based upon an appliedelectric field can be implemented in accordance with various embodimentsof the invention. For instance, FIG. 6 illustrates a portion of across-section of a bottom-gated electrically tunable metasurface inaccordance with an embodiment of the invention. The metasurface issimilar to that seen in FIGS. 5A-5C, except that the antenna is embeddedwithin the Al₂O₃ layer and the ITO layer. In particular, FIG. 6illustrates that the metasurface is characterized by an underlying goldmirror, upon which an Al₂O₃ layer is disposed, upon which a goldsubwavelength antenna element is disposed. An ITO layer is disposed onthe Al₂O₃ layer, and covers the subwavelength antenna element. In theillustrated embodiment, the Al₂O₃ layer is 10 nm thick, the ITO layer is15 nm thick, and the gold subwavelength antenna element is 50 nm thick.Additionally, the planar dimensions of the gold subwavelength antennaelement is 60 nm×90 nm. Note also that a potential difference is appliedin an opposing fashion relative to the conventional application of apotential difference. Of course, as before, while certain dimensions arementioned, it should be clear that any of a variety of geometriessuitable to achieve the desired electromagnetic response can beimplemented in accordance with embodiments of the invention. Moregenerally, any of a variety of layering configurations can beimplemented.

The believed operation dynamics of these described electrically tunablemetasurfaces will now be discussed below.

The Operation of Electrically Tunable Metasurfaces Configured to Respondto Near Optical Frequency Electromagnetic Waves

The believed dynamics of the above-described metasurface tunability areunderstood as follows. When an electric field is applied across thedescribed electrically tunable metasurfaces, the carrier concentrationat the conductor-dielectric interface increases is believed to increaseand forms an accumulation layer. Consequently, this results inmodification of the complex permittivity, which in turn is related to achange in the phase and amplitude of the reflected light.

For example, with respect to the metasurface reflectarray describedabove with respect to FIGS. 5A-5C, using a Drude model to parameterizethe ITO permittivity, it can be shown that when the carrierconcentration in the accumulation layer of the ITO varies from 2×10²⁰cm⁻³ to 1×10²² cm⁻³, the real part of the dielectric permittivity of theactive layer of the ITO can cross zero in the wavelength range betweenapproximately 0.5 μm and 3 μm. When the epsilon-near-zero (ENZ)condition is approached, a large electric field enhancement in theaccumulation layer of the ITO is observed, which can readily beunderstood from the boundary condition imposing continuity of theelectrical displacement at the interface of two materials with differingpermittivities. Accordingly, it is observed that the coupling of the ENZresonance of the ITO with the gap plasmon resonance of the metasurfaceresults in a resonant frequency splitting that can be used for phase andamplitude modulation. This can be illustrated by calculating thereflection coefficient and phase shift of a plane wave reflected from ametasurface. If we assume that the carrier concentration in the bulk ITOis 1×10¹⁹ cm⁻³ and is 1×10²¹ cm⁻³ in the accumulation layer of the ITOwhen the voltage is turned on, resonant frequency splitting can beobserved. FIG. 7A shows that when the voltage is off, the magneticresonance of a metasurface varies from 1000 nm to 1600 nm forsubwavelength antenna elements constructed with lengths from 140 to 220nm. When the voltage is turned on, the plasmonic magnetic resonancecouples with the ENZ region of the active ITO layer, resulting in thesplitting of the magnetic resonance into two resonances. FIG. 7B depictsthis resonance splitting. In particular, the wavelength regime where thereal part of the permittivity, ∈_(r), varies from −1 to 1 ishighlighted. At the wavelengths where the ENZ condition is approached inthe accumulation layer of the ITO, an enhancement of the z-component ofthe electric field E_(z) in the active ITO layer can be observed. When∈_(r) is greater than 0, E_(z) in the accumulation layer of the ITO isparallel to E_(z) in the aluminum oxide and the background ITO. However,when ∈_(r) is less than zero in the accumulation layer, the z-componentbecomes antiparallel to the E_(z) of the surrounding media. FIG. 7Cillustrates the phase shift that occurs when the charge carrierconcentration in the active region of the ITO changes from 1×10¹⁹ cm⁻³to 1×10²¹ cm⁻³ In particular, the dark regions 702 correspond to a 180°phase shift, which overlaps with a −180° phase shift; the arrow 704indicates a positive change in phase shift. For example, starting fromthe bottom of the arrow 704 and moving in the direction of the arrow,the change in phase is from 0° to 180° at the point the dark region 702is reached—which is equivalent to a −180° phase shift. Continuing in thedirection of the upward arrow 704 from the dark region 702, the phaseshift is from −180° to 0°.

FIGS. 8A and 8B illustrate how the reflectance and phase shift vary asfunctions of wavelength and charge carrier concentration. In particular,FIG. 8A illustrates reflection as a function of carrier concentrationand wavelength. FIG. 8B illustrates phase shift as a function of carrierconcentration and wavelength. Similar to before, the dark regions 802correspond to a 180° phase shift, which overlaps with a −180° phaseshift; the arrow 804 indicates a positive change in phase shift. Forexample, starting from the bottom of the arrow 804 and moving in thedirection of the arrow, the change in phase is from 0° to 180° at thepoint the dark region 802 is reached—which is equivalent to a −180°phase shift. Continuing in the direction of the upward arrow 804 fromthe dark region 802, the phase shift is from −180° to 0°.

FIGS. 9A and 9B depict how, for the metasurface illustrated in FIGS.5A-5C, the reflectance efficiency and the phase can be shifted as afunction of carrier concentration. In particular, FIG. 9A illustratesthe reflectance efficiency as a function of carrier concentration withinthe active region of the ITO layer. In general, the reflectanceefficiency is relatively invariant to charge carrier concentration. FIG.9B illustrates the phase shift as a function of carrier concentration.As can be seen, modifying the carrier concentration can be used toimplement virtually any desired phase shift. While certain data has beenpresented for certain parameters, it should be clear that embodiments ofthe invention are not limited to only those metasurfaces that havecharacteristics corresponding with those presented in the data. Data canbe similarly obtained for any of a variety of electrically tunablemetasurfaces in accordance with embodiments of the invention.

The current understanding is that these dynamics underlie the operationof the described electrically tunable metasurfaces. However, as alludedto above, embodiments of the invention are not limited to the actualoccurrences of the described dynamics. The scope of the applicationencompasses the described structures irrespective of the actual dynamicsof their operation.

The Fabrication of Electrically Tunable Metasurfaces Configured toControl the Propogation of Electromagnetic Waves having Wavelengths Lessthan Approximately 10 μm

The above described electrically tunable metasurfaces can bemanufactured in any of a variety of ways. For example, in manyinstances, standard e-beam lithography techniques can be used. Forinstance, the metasurface depicted in FIGS. 5A-5C can be manufacturedusing the following procedure: a 3 nm thick Ni film can be deposited asan adhesion layer, by thermal evaporation on a quartz glass substrate;thermal evaporation can then be used to deposit the 130 nm thick goldmirror; the 16 nm thick ITO layer can be deposited using sputteringtechniques; the 5 nm thick Al₂O₃ layer can be grown by atomic layerdeposition; a 260 nm PMMA bilayer (PMMA-495K and PMMA-950K) can then beused to coat the oxide surface in preparation for deposition of thesubwavelength antenna array; a fishbone structure with a 25 μm×25 μmarea, gold connection, and gold pad can be patterned using an e-beamlithography system (Leica Vistec EBPG 5000+) at an acceleration voltageof 100 keV with 100 pA current (for structure) and 50 nA current (forconnection and pad); after exposure and development, the 50 nm Au filmcan be deposited by e-beam evaporation; the resist can thereafter beremoved. Of course, while one manufacturing technique has beendescribed, any suitable manufacturing techniques for implementing theabove-described structures can be implemented in accordance withembodiments of the invention, and they can be used to fabricateelectrically tunable metasurfaces having any of a variety ofcompositions and any of a variety of geometries. It should not bemisinterpreted that the described electrically tunable metasurfaces canonly be fabricated using the specifically described technique.

As can be inferred from the above discussion, the above-mentionedconcepts can be implemented in a variety of arrangements in accordancewith embodiments of the invention. For example, any of a variety ofsubwavelength antenna element geometries can be incorporated, and any ofa variety of materials can be used. The selection of geometries andmaterials can be based on the desired electromagnetic characteristicresponse for the achieved metasurface. Accordingly, although the presentinvention has been described in certain specific aspects, manyadditional modifications and variations would be apparent to thoseskilled in the art. It is therefore to be understood that the presentinvention may be practiced otherwise than specifically described. Thus,embodiments of the present invention should be considered in allrespects as illustrative and not restrictive.

What claimed is:
 1. An electrically tunable metasurface reflectarraycomprising: a mirrored surface; a conductive layer; a dielectric layer;wherein the conductive layer and the dielectric layer are in directcontact, and thereby define a conductor-dielectric interface; aplurality of subwavelength antenna elements; and an electrical powersource configured to establish a potential difference between at leastone subwavelength antenna element and the mirrored surface; wherein apotential difference between a subwavelength antenna element and themirrored surface applies an electric field to a corresponding region ofthe electrically tunable metasurface reflectarray; wherein any appliedelectric fields in conjunction with the geometry and the materialcomposition of each of the subwavelength antenna elements, theconductive layer, and the dielectric layer, enable the electricallytunable metasurface reflectarray to measurably augment the propagationcharacteristics of incident electromagnetic waves.
 2. The electricallytunable metasurface reflectarray of claim 1 further comprising a secondelectrical power source configured to establish a second potentialdifference between at least one other subwavelength antenna element andthe mirrored surface.
 3. The electrically tunable metasurfacereflectarray of claim 1, wherein the electrical power source isconfigured to establish a plurality of potential differences between aplurality of subwavelength antenna elements and the mirrored surface. 4.The electrically tunable metasurface reflectarray of claim 3, whereinany applied electric fields in conjunction with the geometry and thematerial composition of each of the subwavelength antenna elements, theconductive layer, and the dielectric layer, enable the electricallytunable metasurface reflectarray to measurably augment the propagationcharacteristics of incident electromagnetic waves falling within atleast some portion of the electromagnetic spectrum characterized bywavelengths of less than 10 μm.
 5. The electrically tunable metasurfacereflectarray of claim 4, wherein the at least some portion of theelectromagnetic spectrum is characterized by electromagnetic waveshaving wavelengths less than or equal to wavelengths approximatelycorresponding with those of near infrared electromagnetic waves.
 6. Theelectrically tunable metasurface reflectarray of claim 5, wherein when aregion of the electrically tunable metasurface is exposed to an electricfield, reflected incident electromagnetic waves falling within the atleast some portion of the electromagnetic spectrum exhibit a phase shiftbased on the magnitude of the applied electric field.
 7. Theelectrically tunable metasurface reflectarray of claim 5, wherein the atleast some portion of the electromagnetic spectrum is characterized byelectromagnetic waves having wavelengths approximately correspondingwith those of near infrared electromagnetic waves.
 8. The electricallytunable metasurface reflectarray of claim 5, wherein the at least someportion of the electromagnetic spectrum is characterized byelectromagnetic waves having wavelengths less than or equal towavelengths approximately corresponding with those of visible light. 9.The electrically tunable metasurface reflectarray of claim 8, whereinthe at least some portion of the electromagnetic spectrum ischaracterized by electromagnetic waves having wavelengths approximatelycorresponding with those of visible light.
 10. The electrically tunablemetasurface reflectarray of claim 4, wherein: the conductive layercomprises one of: a nitride based material; silver; copper; gold;aluminum; an alkali metal; an alloy; a transparent conducting alloy; andgraphene.
 11. The electrically tunable metasurface reflectarray of claim4, wherein the conductive layer comprises indium tin oxide.
 12. Theelectrically tunable metasurface reflectarray of claim 11, wherein thedielectric layer comprises a dielectric oxide.
 13. The electricallytunable metasurface reflectarray of claim 12, wherein the dielectriclayer comprises aluminum oxide.
 14. The electrically tunable metasurfacereflectarray of claim 13, wherein: the mirrored surface comprises gold;and at least one of the plurality of subwavelength antenna elementscomprises gold.
 15. The electrically tunable metasurface reflectarray ofclaim 14, wherein when a region of the electrically tunable metasurfacereflectarray is exposed to an electric field, the charge carrierconcentration at the conductor-dielectric interface within that regionis altered based on the magnitude of the applied electric field, andthis alteration causes a phase shift in reflected incidentelectromagnetic waves falling within the at least some portion of theelectromagnetic spectrum.
 16. The electrically tunable metasurfacereflectarray of claim 15, wherein a variation in charge carrierconcentration from 1×10¹⁸ cm⁻³ to 1×10²² cm⁻³ is sufficient to shift thephase of reflected incident electromagnetic waves falling within the atleast some portion of the electromagnetic spectrum by at least 2π. 17.The electrically tunable metasurface reflectarray of claim 15, wherein avariation in charge carrier concentration from 1×10¹⁹ cm⁻³ to 1×10²¹cm⁻³ is sufficient to shift the phase of reflected incidentelectromagnetic waves falling within the at least some portion of theelectromagnetic spectrum by at least 2π.
 18. The electrically tunablemetasurface reflectarray of claim 4, wherein at least one of theplurality of subwavelength antenna elements conforms to a rod-shapedgeometry.
 19. The electrically tunable metasurface reflectarray of claim4, wherein at least one of the plurality of subwavelength antennaelements conforms to a V-shaped geometry.
 20. The electrically tunablemetasurface reflectarray of claim 4, wherein at least one of theplurality of subwavelength antenna elements conforms to a split ringgeometry.
 21. The electrically tunable metasurface reflectarray of claim4, wherein at least two of the plurality of subwavelength antennaelements are connected to the same conductive element, which itself isconnected to the electrical power source.
 22. The electrically tunablemetasurface reflectarray of claim 21, wherein rows of subwavelengthantenna elements are connected to a respective conductive element, whichthemselves are connected to the electrical power source.